where \(\lambda _j\)  are the 3\(\times \) 3 Gell-Mann matrices [1]} and the \(\Delta _j\)  are real coefficients that can be time-dependent. Such Hamiltonian matrices belong to su(3), i.e., the algebra of the group SU(3) [2]}, [3]}. Analytic solutions to the time-dependent Schrödinger equation with the Hamiltonian (REF ) are in general not available, except for Hamiltonians of special form belonging to an su(2) algebra, i.e., the algebra of the group SU(2) [4]}.
In this paper we usually use the large splitting \({\cal D}\)  between the \(M_S=0\)  and \(M_S=\pm 1\)  levels to reduce the problem effectively into a two level problem.
